AbstractWe prove that the inequality∑k=1nxkyk2≤∑k=1nyk∑k=1nα+βkx2kyk∗holds for all natural numbersnand for all real numbersxkandyk(k=1,…,n) with0<x1≤x2/2≤···≤xn/nand0<yn≤yn−1≤···≤y1,if and only ifα≥3/4andβ≥1−α.Inequality (∗) with α=3/4 and β=1/4 refines results given by Liu Zheng (J. Math. Anal. Appl.218(1998), 13–21) and the author (J. Math. Anal. Appl.168(1992), 596–604)
We give some background information about the Cauchy-Schwarz inequality including its history. We th...
AbstractWe prove the following results: (i) Let p⩾1 be a real number and let n⩾2 be an integer. If (...
AbstractThe n-linear Bohnenblust–Hille inequality asserts that there is a constant Cn∈[1,∞) such tha...
AbstractWe prove: If xk and yk (k = 1, …, n) are real numbers satisfying 0 = x0 < x1 ⩽ x22 ⩽ ··· ⩽ x...
AbstractWe prove that the inequality∑k=1nxkyk2≤∑k=1nyk∑k=1nα+βkx2kyk∗holds for all natural numbersna...
The Cauchy-Schwarz inequality is one of the most fundamental inequalities in the world of mathematic...
In this paper, we introduce some new refinements of the famous Cauchy-Schwarz inequality |‹x, y›| ≤...
This article presents a Generalization of the Inequality Cauchy- Bouniakovski-Schwarz
In this paper twelve different proofs are given for the classical Cauchy-Schwarz inequality
Vectors, inequality, Cauchy-SchwarzIf u and v are vectors in Euclidean space, then a special case of...
Abstract. We present several multiplicative and addtive converses of the Cauchy-Schwarz inequality i...
© The Mathematical Association of America. We give a simple proof of an improved version of the Cauc...
AbstractIf A and B are positive semidefinite operators on a Hilbert space and if σ is an operator me...
AbstractFor any unitarily invariant norm on Hilbert-space operators it is shown that for all operato...
AbstractWe prove the following theorem: Let m≥2 be a given integer and let a,b,c be real numbers. Th...
We give some background information about the Cauchy-Schwarz inequality including its history. We th...
AbstractWe prove the following results: (i) Let p⩾1 be a real number and let n⩾2 be an integer. If (...
AbstractThe n-linear Bohnenblust–Hille inequality asserts that there is a constant Cn∈[1,∞) such tha...
AbstractWe prove: If xk and yk (k = 1, …, n) are real numbers satisfying 0 = x0 < x1 ⩽ x22 ⩽ ··· ⩽ x...
AbstractWe prove that the inequality∑k=1nxkyk2≤∑k=1nyk∑k=1nα+βkx2kyk∗holds for all natural numbersna...
The Cauchy-Schwarz inequality is one of the most fundamental inequalities in the world of mathematic...
In this paper, we introduce some new refinements of the famous Cauchy-Schwarz inequality |‹x, y›| ≤...
This article presents a Generalization of the Inequality Cauchy- Bouniakovski-Schwarz
In this paper twelve different proofs are given for the classical Cauchy-Schwarz inequality
Vectors, inequality, Cauchy-SchwarzIf u and v are vectors in Euclidean space, then a special case of...
Abstract. We present several multiplicative and addtive converses of the Cauchy-Schwarz inequality i...
© The Mathematical Association of America. We give a simple proof of an improved version of the Cauc...
AbstractIf A and B are positive semidefinite operators on a Hilbert space and if σ is an operator me...
AbstractFor any unitarily invariant norm on Hilbert-space operators it is shown that for all operato...
AbstractWe prove the following theorem: Let m≥2 be a given integer and let a,b,c be real numbers. Th...
We give some background information about the Cauchy-Schwarz inequality including its history. We th...
AbstractWe prove the following results: (i) Let p⩾1 be a real number and let n⩾2 be an integer. If (...
AbstractThe n-linear Bohnenblust–Hille inequality asserts that there is a constant Cn∈[1,∞) such tha...
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